UC Davis

As machine learning powered decision-making becomes increasingly important in our daily lives, it is imperative to strive for fairness of the underlying data processing. In this work, we apply optimal transport technique to develop provably trustworthy solutions to open challenges in fair machine learning:• (Statistical parity) We first apply the optimal affine transport to approach the post-processing Wasserstein barycenter characterization of the optimal fair L2-objective supervised learning via a pre-processing data deformation. We call it Wasserstein pseudo-barycenter. Then, we prove that the Wasserstein geodesics from learning outcome marginals to their barycenter characterizes the Pareto frontier between L2-loss and total Wasserstein distance among the marginals. Thereby, an application of McCann interpolation generalizes the pseudo-barycenter to a family of data representations via which L2-objective supervised learning algorithms estimate the Pareto frontier. Numerical simulations underscore the advantages: composition flexibility, sensitive information protection, computational efficiency, and applicability to unsupervised learning. • (Compatibility between group and individual fairness) We study the compatibility between the optimal statistical parity solutions and individual fairness. While individual fairness seeks to treat similar individuals similarly, optimal statistical parity aims to provide similar treatment to individuals who share relative similarities within their respective sensitive groups. The two fairness perspectives, while both desirable, often come into conflict. We analyze the existence of this conflict and its potential solution: When there exists a conflict between the two, we first relax the former to the Pareto frontier (optimal trade-off) between L2 error and statistical disparity, and then identify regions along the Pareto frontier that satisfy individual fairness requirements. Lastly, we provide individual fairness guarantees for the composition of a trained model and the optimal post-processing step so that one can determine the compatibility of the post-processed model. • (Equalized odds) We apply conditional Wasserstein barycenter to characterize the optimal solution to odds-equalized data representation, via which a broad family of the trained supervised learning models satisfies equalized odds, under mild assumptions.